CrystEngComm

PAPER

Cite this: CrystEngComm, 2020, 22,

3347

Received 7th January 2020,Accepted 19th April 2020

DOI: 10.1039/d0ce00026d

rsc.li/crystengcomm

A digital workflow from crystallographic structureto single crystal particle attributes for predictingthe formulation properties of terbutaline sulfate†

Thai T. H. Nguyen, *a Robert B. Hammond, a Ioanna D. Styliari, b

Darragh Murnane b and Kevin J. Roberts a

A detailed inter-molecular (synthonic) analysis of terbutaline sulfate, an ionic addition salt for inhalation

drug formulation, is related to its crystal morphology, and through this to the surface chemistry of the habit

faces and surface energy of the whole crystal. Coulombic interactions between the terbutaline cations and

sulfate anions contribute 85% of the lattice energy, hydrogen bonding and dispersion interactions

contribute 15%. Morphological prediction identifies a plate-like morphology composed of the forms {010},

{100}, {001} and {11̄0} in good agreement with crystals grown from solution. Synthonic modelling of the

intermolecular interactions, on a crystal face (hkl)-specific basis, reveals that the surface interactions on the

forms with less, relative surface area: {100}, {001} and {11̄0} manifest a greater surface energy, associated,

notably, with a greater proportion of polar interactions at these surfaces compared to the morphological

dominant {010} surfaces. The predicted total surface energies and their dispersive contributions are found

to be in good agreement with those measured at high surface coverage using inverse gas chromatography

(IGC). The modelling approach is complementary to IGC, as it enables surface sites of lower energy to be

probed, that would require experimentally unachievable surface coverages. The utility of synthonic

modelling, in understanding the surface properties of pharmaceutical materials, is highlighted through a

workflow-based pathway for digital drug product design encompassing molecule structure, intermolecular

packing, crystal morphology, surface energy and formulation properties.

1. Introduction

Tert-Butyl [2-(3,5-dihydroxyphenyl)-2-hydroxyethyl] ammoniumhemisulfate or terbutaline sulfate (TBS) is a β-adrenergicagonist: protonated terbutaline hemisulfate. TBS is present asthe active pharmaceutical ingredient (API) in a number ofcommercial formulations for asthma therapy.1 The compoundhas five crystallographic forms2 including two anhydrousmodifications (A and B), one monohydrate, one higherhydrate and one ethanoic acid solvate.3,4 The stablemodification of TBS is an anhydrate B (Fig. 1) and it is thisstructure which is the subject of the current investigations.Two single-crystal structure determinations are reported foranhydrate B (ZIVKAQ5 and ZIVKAQ01 (ref. 6)) at 293 K which

have similar R-factors (6.23% and 7.30%, respectively).Commercially, TBS is marketed as a racemic compoundwhich decomposes on melting with the melting point beingfound to lie in the range of 258–260 °C.7

The commercial drug formulation typically containsrespirable TBS drug particles that have a particle size of∼1–5 μm, formulated with an α-lactose monohydrate carrier

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a Centre for the Digital Design of Drug Products, School of Chemical and Process

Engineering, University of Leeds, Leeds, LS2 9JT, UK.

E-mail: H.Nguyen1@leeds.ac.ukb School of Life and Medical Sciences, University of Hertfordshire, Hertfordshire

AL10 9AB, UK

† Electronic supplementary information (ESI) available: Additional data andfigures showing full synthon analysis for TBS, together with surface chemistryand the binding sites of polar probe on crystal surfaces of TBS and theexperimental data from IGC measurements. See DOI: 10.1039/d0ce00026d

Fig. 1 Molecular structure of the asymmetric unit of terbutalinesulfate anhydrous form B (ZIVKAQ).5

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crystals having a particle size of 70–140 μm.8–10 Due to theirsmall particle size, respirable API particles display highlycohesive and adhesive behaviour readily tending either toform agglomerates11 or to adhere to the surfaces of excipientmaterials, manufacturing process equipment or inhalerdevice components.12–15 Agglomerated or adhered drugparticles must be re-dispersed effectively upon inhalation inorder to be suitable for lung deposition. Hence, a detailedunderstanding of their surface chemistry and surface energyis important, in terms of determining the magnitude of inter-particulate interactions, for designing better formulations e.g.improving content uniformity, aerosolization and inhaledproduct performance.

Indeed, there have been relatively few studies of theeffect of variations in the particle production processesupon surface crystallinity, particle adhesion and cohesionin terms of the inhalation performance of TBS.10,16,17 Thework carried out so far has not provided any fundamentalinsight as regards the surface properties of TBS from amolecular-scale standpoint, particularly in terms ofcharacterizing the external morphology, surface chemistryand particle surface energy. TBS is an interestingcompound of generic relevance in the field of inhalationpharmaceutics. Detailed knowledge, provided by afundamental intermolecular (synthonic) assessment, candeliver useful baseline data for improved understanding ofinhalation-particle surface properties and associated inter-particle interactions.18

Accurate characterization of particle surface-energies canbe challenging.19–21 For example, sessile-drop contact anglemeasurements on the individual facets of macroscopicsingle-crystals and/or powder compacts via the capillary risemethod have not always been found to provide reliableresults.22,23 Surface energy measurements from inverse gaschromatography (IGC) using both polar and apolarprobes17,24–27 have, however, been found to be particularlyuseful in studies of the crystallinity, surface energy andsurface properties of particles. Elsewhere, work using IGChas revealed a number of problematic issues such as samplepreparation-dependency, large sample sizes (e.g. formicronised materials ∼50–100 mg and for coarse particlesmore than 2 grams of sample are required typically),28 time-utilisation and hence high cost. Variability in IGCmeasurements has been reported previously29–31 and thetechnique, even with finite dilution analysis, has not alwaysbeen found to reliably assess the totality of a powder'ssurface area. The later reflects the technique's tendency topreferentially characterize the higher energy bindingsites.32,33 Hence, if results are to be useful, there is a clearneed for a better molecular-scale understanding of both thesources of variability and the impact of surface properties onIGC measurements.

Previous work by Grimsey et al.34 has shown the utility ofmolecular modelling in terms of understanding the surfacechemistry of drug particles and also, its capability foridentifying the interaction sites of molecular probes involved

in IGC analysis. In this previous work, the micronizedmaterial was examined by making the assumption of particlebreakage parallel to planes having the lowest surfaceattachment energies, i.e. the morphologically dominantcrystal surfaces.35,36 This is despite the possibility thatfracture could take place on non-crystal habit surfaces whichmight in turn have high surface energies and rugosity.37

Molecular dynamics simulations have also been employed tocalculate the surface adsorption energies of the probemolecules,38 giving a reasonably close match to thosedetermined from IGC. However, these studies were onlycarried out for the largest crystal surfaces, i.e. those whichgenerally have the lowest surface energies. So far, no studieshave adopted the holistic approach of integratingcontributions from all the habit faces that comprise theexternal morphology of the crystal.

Synthonic modeling has been exploited extensively toinvestigate lattice energy, attachment energy and for theprediction of crystal morphologies using empirical force-field methods.39–41 The interior and surface properties ofcrystals can be predicted42,43 through calculations of thestrength and direction of the inter-molecular interactionsassociated with the bulk (intrinsic synthons) and surfaceterminated (extrinsic synthons) structures.41,44–47 Theseapproaches have been used to investigate a pharmaceuticalsalt46 and also to examine the cohesivity of APIs andexcipients.18 However, acid addition salts (of which TBS isan example) have not, as of yet, been characterised despitetheir importance as APIs for inhalation drug formulation.Synthonic modelling tools can also predict the surfaceenergy of a crystal and hence provide a clear link to surfaceenergies measured by IGC.48,49 This modelling approach isalso useful in being able to partition the calculated surfaceenergy between the different contributing crystal surfaceplanes (hkl) present on a fully facetted drug particle. Suchattributes have obvious importance in terms of aiding theunderstanding of blending, flow and granulation for bothAPIs and excipients.

In summary, this paper reports an analysis of the keysolid-state synthons, together with the predicted morphology,surface chemistry and surface energy of the morphologicallyimportant crystal surfaces of TBS. This analysis iscomplemented with calculations of solvent probe interactionswith the TBS crystal habit surfaces to relate these both to themeasured surface energies from IGC and to the surfacechemistry that characterizes the crystal morphology.

2. Materials and methods2.1 Materials

The molecular formula of TBS within the asymmetric unit is2ijC12H20NO3]

+ SO42− with molecular mass, Mw = 548.65 g

mol−1.5 The anhydrate form B of TBS crystallises in a triclinicstructure with space group P1̄ with unit cell parameters a =9.968 Å, b = 11.207 Å, c = 13.394 Å, α = 100.86°, β = 104.42°, γ= 101.63° with a tri-ionic (2 cation and 1 anion) asymmetric

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unit5 (see Fig. 1). In this work, the atomic coordinates weretaken from the crystal structure5 with the lower R factor(refcode: ZIVKAQ).

For the experimental work; terbutaline sulfate waspurchased from Sigma Aldrich (purity ≥98%) as a white togrey-white crystalline powder for crystallisation experiments.For surface energy measurements, terbutaline sulfate (batchAAEX) was kindly provided by AstraZeneca (Mölndal,Sweden), and was used as supplied.

2.2 Crystal growth

As received TBS was purified by recrystallization. TBS singlecrystals were prepared by cooling crystallisation as follows:0.32 g of TBS were added to a mixture of 70% water and30% ethanol (% by mass) to make up 1 g of solution. Thiswas then heated to 70 °C and stirred for 30 minutes toensure complete solute dissolution and then cooled to 5 °Cand left for 2–3 days until crystallization occurred. AnOlympus BX51 microscope, with a UMPlanFl 10×/0.30objective was used to characterize the size and shape of theresultant crystals.

2.3 Surface energy measurements

Specific surface area (SSABET) and surface energy (SE) analysiswas conducted using a surface energy analyser (iGC-SEA,Surface Measurement Systems Ltd, UK; https://www.surfacemeasurementsystems.com/products/igc-sea/).

0.247 g of terbutaline sulfate was packed into a silanisedglass iGC column (internal diameter 4 mm). Prior to anymeasurements, the loaded column was conditioned usinghelium carrier gas at 10 scc min−1 for 2 h at 30 °C and 0%RH. Methane gas was injected at the start and the end of theexperiments for the dead volume calculation. SSABET wascalculated via Brunauer–Emmett–Teller (BET) theory, basedon the n-octane adsorption isotherm data and using the peakmax parameter.18

For the surface energy, the columns were equilibrated asmentioned above. Non-polar probes (n-decane, n-nonane,n-octane and n-heptane) and polar probes (chloroform,toluene, ethyl acetate and acetone) were injected into thecolumn at concentrations consistent with a range of surfacecoverages (n/nm, between 0.5 up to 13% for all probes withthe exception of n-decane that reached maximum surfacecoverage at 4.5%). Based upon an analysis method previouslyreported,50,51 the dispersive (γd, non-polar) and acid–base(γab, polar) components of the surface energy were calculatedusing the Dorris–Gray method and the peak centre of massparameter. This is based on a linear fit on the 4 alkaneprobes for surface coverages 0.5–4.5% and based on 3alkanes for surface coverages above 4.5%. Specific freeenergies of adsorption (ΔGSP) of the monopolar probes wereobtained using the polarisation approach52 and the peakcentre of mass parameter. All measurements were made intriplicate.

2.4 Computational modelling methodology

The computational analysis was carried out utilizing theCambridge Crystallographic Data Centre (CCDC) materialsMercury,53 BIOVIA Materials Studio,54 HABIT98 (ref. 39) andSystSearch55,56 software. Partial atomic-charges werecalculated using the semi-empirical quantum mechanicsprogram MOPAC57 utilizing the Austin model 1(AM1)approach. The energetic strength and chemical identity ofthe intermolecular synthons, the lattice energy (Elatt or Ecr),and, hence, the slice (Esl) and attachment (Eatt) energies werecalculated with HABIT98.39 This was aided by a detailanalysis of the intermolecular interactions (synthons), bothwithin the bulk structure and on the crystal habit faces,which was complemented by molecular-scale visualization ofthe bulk and surface chemistry. The digital workflowsummarized in Fig. 2 provides an overview of the mainfeatures of the analysis used.

2.4.1 Calculation of bulk (intrinsic) synthons and latticeenergy determination. The lattice energy was calculated usingpotential parameters from Tripos 5.2,58 which employs anempirical interatomic potential, Lennard Jones 6–12potential, see eqn (1), with a scaling factor for hydrogen-bonds, together with the Evjen summation method59 toensure convergence of the coulombic energy summation.

Ecr ¼ 12

XN

k¼1

Xn

i¼1

Xn′

j¼1

− Aijrij6

þ Bij

rij12þ qiqj

rij(1)

where A and B are atom–atom parameters, i is an atom in thecentral molecule, j is an atom in the kth surroundingmolecule, N is number of surrounding molecules, n is totalnumber of atoms in the central molecule, n′, is total numberof atoms in each of the surrounding molecule, qi and qj arepartial, atomic point charges on atoms i and j, and rij isinter-atomic distance between atoms i and j.

The lattice energy was calculated using spherical radii, forcut-off of the energy summation, between 5 and 50 Å, in 5 Åsteps, to test and ensure convergence of the lattice energy.The calculation was repeated for each molecule in theasymmetric unit and the results were averaged over all sitesin the asymmetric unit and then averaged over both theasymmetric units in the unit cell.

2.4.2 Calculation of surface (extrinsic) synthons andmorphological prediction. The pairwise intermolecularinteraction energies between a central asymmetric unit in thecrystal lattice and all the surrounding asymmetric units,contributing to the lattice energy summation, werepartitioned into slice and attachment energy contributions,according to eqn (2). If the centre of coordinates of theremote asymmetric unit was within the region bounded byadjacent Miller planes (hkl), separated by the inter-planarspacing dhkl, then the associated pairwise interaction-energyis regarded as contributing to the slice energy (Ehklsl ) for thatcrystal surface plane (hkl) orientation. Conversely, if theremote asymmetric unit is centred outside this region the

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associated interaction energy is taken to contribute to theattachment energy Ehklatt .

Ecr = Ehklatt + Ehklsl (2)

The attachment energies were normalised to that calculatedfor the slowest growing face, i.e. with the largest surface areato determine relative growth rates per surface. The Mercurysoftware was used to construct a Wulff plot60 and, throughthis, a prediction of the crystal habit based on theattachment energy model was generated. The latter assumesthat the relative growth rate (Rhkl) of a given crystal surface(hkl) can be taken, at low supersaturation, to be proportionalto Ehklatt ,

44,61,62 see eqn (3).

Rhkl ∼ Ehklatt (3)

The morphological predictions were crossed-validatedthrough experimental studies of the observed crystals asobtained using cooling crystallisation techniques (see section2.2).

The anisotropy factors for the crystal habit surfaces werecalculated using eqn (4),

ξhkl ¼Esl

Ecr(4)

where the anisotropy factor, ξhkl, provides a useful indicationregarding the degree of synthon saturation due to surfacetermination effects.63–65 The anisotropy factor provides ameasure of the fraction of intermolecular interactions thatare saturated, for a molecule exposed on a particular crystalsurface (hkl), when compared to same molecule within thebulk crystal structure.

2.4.3 Calculation of surface energy. The surface energy(SE) of crystal surfaces was calculated from the attachmentenergy of individual crystal surfaces62 using eqn (5).

γhkl ¼Z × dhkl × Ehkl

att

�� ��2 × NA ×V

(5)

where Z is the number of molecules per unit cell, dhkl is thethickness of the growth step layer, NA is Avogadro's constant,and V is the unit cell volume. The dispersive and polarcomponents of the surface energy were calculated from thesurface energy contribution from the van der Waals andcoulombic components, respectively.

The overall particle surface energy (γparticle)49 was

calculated using eqn (6), as a surface area weighted averagebased on the attachment energy.

γparticle ¼Xn

i¼1

γhkli × Ahkli × Mhkl

i (6)

Here n is the number of forms ({hkl}, i.e. family of faces), γhkli

is surface energy of individual crystal surfaces, Ahkli is thefractional surface area of the habit face and Mhkl

i is themultiplicity of the habit face.

2.4.4 Calculation of interaction energies for heterogeneousprobe molecules on the crystal surfaces. The binding ofheterogeneous probe molecules on the crystal habit surfaceswas predicted using systematic grid search methods,18,66–69

using the SystSearch18 program. The model is based on acalculation of the rigid body intermolecular interactionenergies between selected probe molecules and crystalsurfaces. This involves the generation of a three-dimensionalgrid adjacent to the model of the crystal surface with theinteraction energies being calculated by locating the probemolecule at every grid point on and above the surface wherethe probe is rotated through a grid of points in a rotationalEulerian space. The calculations of the interaction energieswere carried out without surface relaxation using theDreiding II atomic force field,70 and with partial chargescalculated using the MOPAC method.57 The forcefield

Fig. 2 A digital workflow from crystallographic structure to particle properties for the prediction of the formulation properties.

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contains separate functions for calculating the van der Waals(dispersive), hydrogen bonding (H-bonding) and coulombicinteractions and hence the respective contributions fromeach type of these interactions to the total intermolecularinteraction was quantified. A more comprehensivedescription of this methodology was provided byRamachandran, V., et al.18 From this, the strongestinteraction (most negative interaction energy) and the meaninteraction energy from the histogrammic distribution‘finger-print’ was calculated for each crystal habit surface(hkl).

3. Results and discussion

Results from the molecular and synthonic modelling analysisare described in sections 3.1 and 3.2, the morphologicalanalysis and surface chemistry are presented in section 3.3and 3.4, the comparison of the calculated surface energies

with those measured using IGC is given in section 3.5 andthe cross-correlation of the IGC data with intermolecularbinding energies is given in section 3.6.

3.1 Analysis of intermolecular packing within the bulk crystalstructure

The intermolecular packing and crystal chemistry of TBS issummarised in Fig. 3 and Table 1.

The terbutaline cations have an asymmetric centre atcarbon atom C7 and C19 for terbutaline cation 1 (TB I) andterbutaline cation 2 (TB II), respectively. The terbutalinecations consist of phenethylamine (C6H5–CH2–CH2–NH2–)groups in which the nitrogen atoms N1 and N2 areprotonated (see Fig. 1). Each terbutaline consists of threealcohol groups (two –OH groups attached the benzene ringand one –OH group attached to the alkyl chain) and oneamine –NH2 group. The asymmetric unit contains two

Fig. 3 (a) Intermolecular coordination hydrogen-bonding shell for the TB I cation highlighting 7 H-bonding interactions with 4 other ionsassociated with cation TB I and cation TB II and 2 divalent sulfate counter anions; (b) intermolecular coordination hydrogen bonding shell for theTB II cation highlighting 7 H-bonding interactions with 5 other ions associated with cation TB I and cation TB II and 3 divalent sulfate counteranions; (c) intermolecular coordination hydrogen bonding shell for the SO4

2− group highlighting six H-bonds formed with 2 TB I and 3 TB II; (d)intermolecular packing showing terbutaline pack in alternate layers of terbutaline cation TB I (red) and cation TB II (blue).

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terbutaline cations and one sulfate anion. The twocrystallographically inequivalent terbutaline ions (TB I andTB II) exhibit differences in their conformation reflectingdifferent rotations of the tertiary-butyl group about theconnecting nitrogen to carbon covalent bond (NH2–C–(CH3)3groups).

The basic unit of the crystal structure is an inversion-related terbutaline ion TB I dimer formed between the amineand alcohol groups attached to the alkyl chain. Eachterbutaline cations TB I is bonded to one cation TB I, onecation TB II and two sulfate anions (Fig. 3a). Each cation TBII is bonded with one cation TB I and one cation TB II and 3divalent sulfate anions (Fig. 3b).

In the crystal structure, each sulfate anion forms sixhydrogen bonds with five TB cations (Fig. 3c) (two TB I andthree TB II, one of the two, TB I, forms 2 hydrogen bondswith the sulfate group through N–H⋯O–S and O–H⋯O–S)utilizing six of the eight potential hydrogen bond acceptorsfrom sulfate group. Each TB cation donates five (from three–OH groups and one –NH2 group in each TB cation) andaccepts two hydrogen bonds (from two –OH groups).

In summary, there is a strong hydrogen bond networkwithin the TBS crystal structure, with the use of all ten thehydrogen bond donors. However, not all the potentialhydrogen bonding acceptor sites are used in the crystalstructure, with four acceptors from TB I and TB II (two nitrogenatoms in the –NH2 group and two oxygens in the –OH group)and two acceptors from sulfate group are being unsaturated.

3.2 Lattice energy and identification of key bulk intrinsicsynthons

Partial atomic-charges, calculated using the semi-empiricalquantum mechanics program MOPAC, are provided in the

section S1 in the (ESI†). Summation of the intermolecularinteractions with distance revealed convergence at 15 Å to alattice energy of −138.88 kcal mol−1 of asymmetric units withthe coulombic interactions accounting for ∼85% of thelattice energy (Fig. 4). To the authors' knowledge, nosublimation enthalpy data has been published for TBS withwhich to compare to the calculated lattice energy. Thesummation of the percentage contribution to the latticeenergy from the different molecular groups of theasymmetric unit, revealed that, TB I and TB II groupscontributed 18.4% and 22.8% respectively, whilst the SO4

2−

group was found to make the greatest contribution ca. 58.8%reflecting its intimate involvement with the strong coulombicanion–cation interactions.

Table 2 lists the top nine strongest, attractive intrinsicsynthons found from the analysis of the bulk crystal structureand highlights the component of ions in the attractivesynthons (with subscript a). All of the most attractivesynthons were found to be between the sulphate anion –

terbutaline cation pairs, indicating that the strongestinteractions within crystal lattice are a result of thecoulombic forces. Also, due to the symmetrical inequivalenceof the terbutaline cation pairs, the synthon types found arequite similar to each other and simply occur between thedifferent symmetrically inequivalent ions.

Fig. 5 reveals that the orientation of specific atomicgroups, particularly the –OH and –NH2 functional groupsstrongly influences the strength of the synthon. Synthons Aa,Ba, Ca and Da (interactions between sulfate with TB I or TB II)have the closest orientation of the oppositely charged SO4

2−

and –NH2+, resulting in a very strong coulombic

interaction. For synthon Aa and Ba (interaction betweensulfate and TB II), the H-bonding is formed due to theclose proximity of the donor H on the NH2

+ group andthe acceptor O on the SO4

2− group. For the synthon Ca

and Da (interaction between sulfate and TB I) theH-bonding is formed due to the close proximity of thedonor hydrogen atoms on the NH2

+ and –OH group andacceptor oxygen atoms on the SO4

2− group. The addedattractive force of these H-bonds probably contributes tothis synthon being calculated to be the most attractiveinteraction within the structure. It was also observed, asexpected that, in general, as the distance between theSO4

2− and NH2+ groups increases, the attractive force

between the ions decreases; for example distance betweensulfur of SO4

2− and nitrogen NH2+ of synthon Aa and Ba

decrease from 5.48 to 4.36 Å; the attractive forceincreases −2.05 to −2.59 kcal mol−1. However, although

Fig. 4 Lattice energy convergence as a function of limiting radius forTBS indicating that interactions at a distance greater thanapproximately 20 Å make a relatively small contribution to the latticeenergy.

Table 1 Molecular descriptors for TBS formula unit (two terbutaline cations and one sulfate anion) and crystal descriptors (with the numbers ofhydrogen bond acceptors and donors utilised within the crystal structure)

Property

Molecular descriptor Crystal descriptor

Two TB cations Sulfate cation TB I TB II Sulfate anion

Number of hydrogen bond acceptors 8 8 2 2 6Number of hydrogen bond donors 10 0 5 5 0

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the SO42− and the NH2

+ groups are closer in synthon La,synthons Ia/Ka and Ja were found to have a greaterattractive interaction due to these synthons forming moresignificant van der Waals and H-bonding interactions,respectively.

The strongest repulsions within the crystal structure werefound to be between the sulfate anions (see ESI,† section S2).Due to the symmetrical equivalence of the anions, the fourmost-repulsive, independent pairs only are illustrated.Table 2 lists that, as expected, the majority of the repulsionenergy is due to the coulombic repulsions. These strongestrepulsive synthons were found to be between 6.43–9.48 Åapart (S–S). These repulsions were more than compensatedfor by the strong attractive forces between the anion–cationpairs.

3.3 Predicted morphology and identification of key surface-terminated extrinsic synthons

The predicted morphology, shown in Fig. 6(a) and detailed inTable 3 column 1–6 based on the attachment energy model,shows a plate-like morphology with the {010} being thedominant form, along with the smaller {100}, {001} and {11̄0}surfaces. The predicted morphology agrees well with theobserved experimental crystal morphology of TBS crystalsgrown in a mixture of 70% water and 30% ethanol at 5 °C(see Fig. 6(b)).

The percentage surface saturation (anisotropy factors) arelisted in Table 3 column 7. As expected, the {010} surfacecontains the highest degree of saturation, 96.28%, due tofewer strong synthons being broken at the surface. In

Table 2 Strength of top nine most attractive (with subscript a) and 4 most repulsive synthons (with subscript r) along with synthon analysis for the{010}, {100}, and {001} and {1−10} crystal surfaces. Distances quoted are the distances between the two centres of gravity of the ions. Note that SFindicates sulfate groups and TBI and TB II are terbutaline cations 1 and 2, respectively; SL is slice and ATT is attachment

SynthonIonsinvolved

Inter-iondistance (Å)

Van der Waals contribution(kcal mol−1)

Coulombic contribution(kcal mol−1)

Total interaction(kcal mol−1) {010} {100} {001} {1−10}

Aa SF/TB II 5.48 −1.30 −86.33 −87.63 SL SL SL SLBa SF/TB II 4.36 −1.54 −80.70 −82.24 SL SL SL SLCa SF/TB I 5.04 −1.68 −77.31 −78.99 SL SL ATT SLDa SF/TB I 4.81 −0.89 −74.39 −75.28 SL SL SL SLEa SF/TB I 6.56 −0.31 −48.14 −48.45 SL ATT SL ATTFa SF/TB II 8.57 −0.17 −41.20 −41.37 ATT SL SL ATTGa SF/TB II 7.50 −0.77 −38.23 −39.00 SL ATT SL ATTHa SF/TB II 9.66 −0.03 −36.77 −36.80 SL SL SL SLIa SF/TB II 12.31 −0.01 −32.50 −32.51 SL SL ATT SLAr SF/SF 6.43 −0.10 106.96 106.86 SL SL SL SLBr SF/SF 8.19 −0.02 81.20 81.18 SL SL ATT SLCr SF/SF 9.26 −0.01 71.93 71.92 SL ATT ATT ATTDr SF/SF 9.47 0.00 70.05 70.05 ATT SL SL ATT

Fig. 5 Molecular orientation of the top six (Aa, Ba, Ca, Da, Ea and Fa) attractive synthons shown in Table 2 indicating that the major interactions arebetween the oppositely charged ions. Similar interaction types that are only different because they are between the different terbutaline cationstype I and type II all distances are quoted between S in SO4

2− and N in NH2+. The dotted blue lines indicate the hydrogen bonds.

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comparison, the {100}, {001} and {11̄0} surfaces have 92.3%,87.6% and 92.03% saturation, respectively; as they arepredicted to have strong anion/cation synthons broken attheir respective surfaces. This agrees with the dominant facesrank order {11̄0} < {001} < {100} < {010}.

In this study the synthons that are predicted to contributeto the attachment energy, and hence growth, of a givencrystal surface have been identified and displayed in Table 2.This reveals that stronger intermolecular interactions(synthons) contributing to the attachment energy Eatt of thecrystal faces {hkl} leads to the higher growth rates of {hkl}.The strongest interaction contributing to the attachmentenergy at the {010} surface was found to be synthon Fa(−41.37 kcal mol−1) (see Table 2), which is the coulombicinteraction between sulfate and amine group of terbutalinecation 2. The strongest interactions contributing to theattachment energy at the {11̄0} surface were found to be Ea,Fa, and Ga (−48.45, −41.37 and −39.00 kcal mol−1). Thesepredictions are consistent with the morphological dominanceof this face and with the order of the importance of the faces:{11̄0} < {001} < {100} < {010}.

3.4 Analysis of the surface chemistry of the habit planes

The morphology of a crystal in different growth environmentsdepends, collectively, on the relative growth rates associatedwith its constituent crystal-habit faces. Ultimately these ratesare linked to the respective interaction energies associatedwith the strongest synthons on these surfaces. The growthmorphology in a vacuum of an individual habit face can berationalised in terms of the respective molecular

arrangements, and hence synthon orientation, on thesespecific faces. Hence, molecular modelling can be utilised toexamine the surface chemistry of the {010}, {100}, {001} and{11̄0} surfaces. For the faces listed in Table 3, the extrinsicsynthons identified as contributing to the attachmentenergies were labelled on molecular models of the surface asshown in the section S3 in the ESI.†

The {010} form exhibits one –OH group from eachterbutaline cation exposed on the surfaces with all theH-bonding being embedded within crystal surfaces. Thesurfaces of the forms {100} and {001} exhibit two –OH groupsone each from each terbutaline cation exposed on thesurfaces; however, the {001} surfaces have non-bondedH-bond acceptor groups across the surface which areavailable to form hydrogen bonds with probe molecules. The{11̄0} morphological form exposes three –OH groups and theprotonated –NH2–C3H9 moiety on the crystal surface. Thisindicates that these faces are more polar than the other facesand explains the ranking of the morphological importance ofthe exposed crystal surfaces in terms of surface area.

3.5 Comparison of predicted cumulative particle surfaceenergies with measured IGC data

The surface energies, as a function of surface plane, togetherwith the fractional surface areas of the associated habit planeare given in Table 3, columns 9 and 4, respectively. Thepredicted cumulative surface energies and the measuredsurface energies of non-micronized TBS, as measured by IGC,are reported in Table 4 and Fig. 7. The dispersive componentof the surface energy measured by IGC ranges between 49.1

Fig. 6 Predicted morphology using attachment energy model showing a plate-like crystal morphology with the {010} being the dominant form,along with the smaller {100}, {001} and {11̄0} surfaces (a) and experimentally observed morphology of TBS single crystals (b).

Table 3 List of crystal surfaces, attachment energies, surface area and surface saturation for TBS crystal

Crystalface Multiplicity

Interplannarspacing dhkl(Angstrom)

Surface areaAhkl (%)

Slice energy Esl(kcal mol−1)

Attachmentenergy Eatt(kcal mol−1)

Surface saturationζhkl (%)

Dispersive surfaceenergy (mJ m−2)

Total surfaceenergy (mJ m−2)

{010} 2 10.62 26.33 −133.72 −5.16 96.28 23.24 27.73{100} 2 9.31 10.29 −128.15 −10.73 92.27 31.44 50.57{001} 2 12.55 8.69 −121.71 −17.16 87.64 38.99 108.97{11̄0} 2 8.14 4.70 −127.81 −11.07 92.03 29.61 45.57

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and 32.8 mJ m−2; this is comparable to measured values ofmicronized and supercritical processed TBS reported byRehman, M. et al.71 (58.61 ± 0.3 for the micronized and55.05–57.37 for the supercritical processed material).

The predicted surface energy showed significantdifferences between the surface energies of individual crystalsurfaces (see Table 3, columns 8 and 9). The surface energiesof the {11̄0} and {001} forms are greatest whilst the surfaceenergy of the {010} form is smallest. This agrees with thesurface chemistry analysis which indicates that the {11̄0} and{001} forms have more polar and non-polar componentsexposed on the surfaces contributing to the dispersive andpolar surface energy, for example, for the {11̄0} faces the –

CH3–CH3–CH3 and –CH2 group (alkyl groups) attached to the–NH2 contribute to dispersive energy components and –NH3

and three –OH groups contribute to polar surface energycomponents.

The predicted surface energy, which is based upon anidealised perfect termination of the bulk crystal lattice, gavesmaller values than those measured for TBS supplied fromAZ (see Table 4) and those measured for micronized andprocessed TBS reported by Rehman, M. et al.71 It has beenreported that IGC performed in the infinite dilution regimeusually yields higher values of dispersive surface energy thanother measurement techniques,72 as well as sometimesproviding an unrepresentative measure of the majority of thepowder surface area. Infinite dilution IGC, historicallyperformed at 0.03 p/p0, has been shown to probe the crystalsurface regions with the highest energy, while finite dilution

IGC can provide a surface heterogeneity map.32,73–75 Theeffectiveness of infinite dilution IGC is likely due to adsorbedmolecules having no other adsorbate molecules close enoughto allow any adsorbate–adsorbate interactions, hence there isa lack of competition for adsorbate binding sites. The highestenergetic sites probed by infinite dilution IGC may notdominate the inter-particulate contact areas, since theirrelative contribution to the total particle surface area may beexceedingly low. For example, for TBS the {001} facescontribute the highest surface energy (Table 3), but this faceonly provides 8.69% of the crystal surface area (Table 3).

It was previously reported33,76 that size reduction, such asmicronization, leads to an increase in the measureddispersive surface energy of the drug substance withincreasing extent of micronization. The increase in surfaceenergy is probably due to the generation of new, higherenergy sites of crystalline disorder due to impaction events orparticle fracture.33 Infinite dilution IGC measurement ofsurface energy would therefore be expected to be dominatedby the latter, unrepresentative high energy sites.

It is significant that computational prediction of surfaceenergy for the highest energy sites (the {001} surfaces: 109 mJm−2) correlated well with the experimental measurements atlow surface coverage (103.3 mJ m−2), where the highestenergy surface sites are probed (both from the standpoint ofcrystallography and process-induced disorder). It was evidentthat the surface energy values determined experimentally forthe highest surface coverage (which should probe therelatively lower surface energy sites) showed an improved

Table 4 Comparison of predicted surface area weighted whole particle surface energy of TBS compared with those measured using IGC

Surface energy Dispersive SE (mJ m−2) Total SE (mJ m−2)

Calculated surface energy (weighting with % surface area) (mJ m−2) 28.27 48.2Surface energy measured by IGC for surface coverage [0.5–13%] 49.1–32.8 103.3–64.7

Fig. 7 Relative pressure reached during the IGC experiments as a function of the surface coverage for the alkane probes (a); measured dispersiveand total surface energy of non-micronized terbutaline sulfate supplied by AZ using IGC showing the surface energy decrease with increasingsurface coverage (b).

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correlation with the average calculated surface energy whenthis is weighted with respect to the relative contribution ofeach crystal face to the total surface area of the crystal (seeTable 4).

3.6 Comparison of the predicted adsorption energy for thedifferent polar probes with those measured using IGC

The results for the grid-search modelling are given in Fig. 8.These provide histograms of calculated interaction energies fora series of probe vapours (chloroform, toluene, acetone, andethyl acetate) on TBS crystal surfaces {010}, {100}, {001} and{11̄0}. The strongest interaction energies, the mean interactionenergy distribution of a probe molecule on TBS crystal surfaces,together with the total interaction energy of probe molecules onthe TBS particles are summarized in Table 5.

This study elucidates the anisotropic surface chemistryof the major faces of TBS, identifies that polar solvent-probe molecules were found to interact more strongly withthe side faces {100}, {11̄0} and {001} and least with thelarge {010} surface. This illustrates that the relativecontribution of a crystallographic face to its total surfacearea plays an important role in the preferential bindingsite for the probe molecules. Indeed, the modelling

studies indicated that the surface roughness at themolecular-level can have a major influence on the probemolecule adsorption energies, which may impact theactual process of adsorption in experimentaldeterminations. This increased surface roughness can beexpected to provide a favourable docking site foradsorption in a surface ‘valley’, for the probe molecules.Hence, it has been shown that the higher interactionenergy sites for the {100}, {001} and {11̄0} surfaces tendto be located in the surface ‘valleys’. Particularly for the{11̄0} surface, the probe molecules prefer to bind in achannel present at the crystal surfaces, which is also thecase for ethyl acetate, chloroform and toluene probemolecules, resulting in high interaction energies at thissurface. Further details for the preferred binding positionof the probe molecules on the TBS crystal surfaces arepresented in the ESI† (see section S4).

The data analysis also elucidated that for toluene andchloroform, the solvent probe interactions with all thesurfaces are found to be almost completely from dispersiveforce contributions and coulombic interactions (forchloroform), without a hydrogen bonding contribution.However, it should be noted that in a real solvent system,chloroform is known to form weak hydrogen bonds, the

Fig. 8 Histogram of interaction energy distribution of (a) ethyl acetate, (b) chloroform, (c) acetone and (d) toluene of crystal surfaces of {010}(black), {100} (red), {001} (green) and {11̄0} (blue) of TBS showing binding energies of probe molecules are different on individual crystal surfaces(with bin size 2 kJ mol−1).

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Dreiding forcefield used in these calculations does notconsider chlorine as a hydrogen bond acceptor atom andhence no hydrogen bonding contribution would be expected.Similarly, toluene as a non-polar solvent molecule, isincapable of forming hydrogen bonds so would also beexpected to have zero contribution to the overall interactionenergy. In contrast, for ethyl acetate and acetone, theinteraction energies are found to have had a significantH-bonding contribution and, additionally, the coulombicenergy contribution is significant, particularly for acetone.

The measured specific surface energies ΔGSP (kJ mol−1)using chloroform, toluene, ethyl acetate, and acetone aregiven in Fig. 9.

Despite the poorer agreement, a trend of decreasingmeasured surface energy was apparent as surface coverage wasincreased, probing the lower surface energy sites (see Fig. 7band 9b). The trend for surface energy in Fig. 9 indicates that

the surface energy distribution of TBS is quite heterogeneous.During the finite dilution IGC experiments, the surface energydistribution was calculated via the retention volumes of theprobes at a specific surface coverage in order to allow for thedifferences between the various probes. However, this is also alimitation of the technique as the maximum injectableamount – and as such the maximum surface coverage aselected probe can achieve – is determined by the probe'scross-sectional area. In this present work, it was not possibleto measure the dispersive component of TBS surface energyaccurately above surface coverages of 13% as that wouldreduce the number of available alkane probes to two (octaneand heptane), insufficient for accurate linear regression.Further analysis of the adsorption isotherms of the probes (seeFig. 7a and 9a, and section S5 in the ESI† for the adsorptionisotherms) showed that even at the surface coverage of 13%,the partial pressure in the column did not exceed 0.06 P/P0

Table 5 Strongest (best binding position), mean and total interaction energies of a probe molecule on TBS crystal surface alongside the surface freeenergies of adsorption as measured from IGC at 0.5% and 13% of surface coverage

Maximum and mean interactionenergies of a probe molecule onTBS crystal surfaces (kJ mol−1)

Total interaction energyweighted with % surfacearea of individual crystalsurfaces (kJ mol−1)

Surface free energies ofadsorption (−ΔGSP) (kJ mol−1)measured by IGC

Probe molecules {010} {100} {001} {11̄0} 0.5% surface coverage 13% surface coverage

Ethyl acetateMaximum −27.68 −33.49 −46.73 −52.16 −34.49 15.85 ± 0.04 11.17 ± 0.45Mean −10.71 −10.06 −15.28 −13.78 −12.17ChloroformMaximum −18.65 −28.38 −21.31 −30.55 −22.24 7.88 ± 0.03 5.61 ± 0.36Mean −9.83 −11.09 −11.61 −12.74 −10.68AcetoneMaximum −24.93 −32.09 −40.55 −43.02 −30.82 17.02 ± 0.05 11.19 ± 0.5Mean −10.34 −11.94 −15.43 −13.94 −11.89TolueneMaximum −18.91 −25.83 −24.22 −29.20 −22.41 4.58 ± 0.02 3.77 ± 0.16Mean −10.23 −11.22 −11.77 −12.59 −10.93

Fig. 9 Relative pressure reached during the IGC experiments as a function of the surface coverage for the polar probes (a); the measured surfacefree energies of adsorption ΔGSP (kJ mol−1) using chloroform, toluene, ethyl acetate, and acetone (b).

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which indicates that a full monolayer coverage has not beenreached and thus only a fraction of the heterogeneous surfacewas probed. Consequently, this would suggest that theexperimental surface energy measurements by IGC did notachieve sufficient surface coverage to probe the lowest surfaceenergy sites in the same way as have been predicted in themolecular modelling-based grid search approach.

4. Conclusions

In this work, molecular and synthonic modelling tools havebeen successfully applied to link dominant synthoncontributions, the percentage surface saturation, the surfacearea, surface chemistry analysis (functional groups exposedon crystal surfaces, extrinsic synthons) surface energy andphysical properties. Synthonic modeling revealed the extentof the importance of coulombic interactions between the saltpairs to stabilize the lattice energy, compared with small, freebase, molecule crystal structures. Attachment energymorphology predictions produced a plate-like morphologywith the {010} being the dominant form, along with thesmaller {100}, {11̄0}, {101} and {001} forms, which isconsistent with the crystal morphology observed fromsolution grown crystals. The synthon analysis explains whythe relative morphological importance to the crystalmorphology of forms is in the order {11̄0} < {001} < {100} <{010}. The faster growing {11̄0} surfaces were predicted tohave many more of the strong synthons notably Ea, Fa and Ga

contributing to their attachment energy.The calculated dispersive and total surface energy had

lower values than the measured data reported in this studyand tended to correlate better at a surface coverage of 13%compared to 0.5% surface coverage. This might be due to theexperimental surface energy measurements by IGC in thisstudy which did not achieve sufficient surface coverage toprobe all the lowest surface-energy sites, combined with thefinding that the surface energy distribution of TBS across itsdifferent crystal habit faces is quite heterogeneous. From thecalculated adsorption energy for the different polar probeson TBS crystals, the mean interaction energy was found toprovide a better correlation with the measured surface freeenergies of adsorption (−ΔGSP).

The calculated surface energy analysis was found to be veryhelpful for assessing and interpreting the measured IGC data,notably through its ability to both partition surface energiesbetween the different morphological forms as well as probelower energy binding sites not routinely accessible using IGC,for designing formulation processes for inhalation drugs.This is due to the importance of surface properties, their linkto drug particulate-interactions and the associated, intrinsic,powder properties needed for achieving effective drugaerosolization, efficacy, lung delivery and therapeutic success.This suggests that the type of analysis presented here mighthave more general applications in the formulation design ofother APIs in order to understand, in-detail, the fundamentalmaterial behavior at the molecular scale.

List of symbols

Elatt Lattice energyEsl Slice energyEatt Attachment energyξhkl Anisotropy factorsZ The number of molecules per unit celldhkl The thickness of the growth step layerNA Avogadro's constantV The unit cell volumeγ Surface energyγd Dispersive components of surface energy (non-polar)γab Polar components of the surface energy (acid–base)ΔGSP Specific free energies of desorption

Glossary of terms

vdW Van der WaalsH-Bonding Hydrogen bondingSynthons Pairwise intermolecular interactionsIntrinsic synthons Fully saturated synthons found in the

bulk of the crystal structureExtrinsic synthons Unsaturated synthons due to surface

termination of the crystal structureLattice energy Strength of the intermolecular

interactions within the crystal structureper mol

Slice energy Energy of intermolecular interactionsfound within one d-spacing on the (hkl)crystallographic plane

Attachment energy Energy of intermolecular interactionsformed when a crystal slab oned-spacing thick, defined by (hkl) plane, isinserted into a bulk crystal structure

Anisotropy factor The degree of saturation of a moleculeexposed at a cleaved crystal surface (hkl),in comparison to the same moleculefully saturated in the bulk structure

Conflicts of interest

The authors declare no competing finance interest.

Acknowledgements

This work was supported by the UK's EPSRC research grant EP/N025075/1 INFORM2020 “Molecules to manufacture: Processingand Formulation Engineering of Inhalable Nanoaggregates andMicro-particles”. This work also builds upon research onmorphological modelling supported by EPSRC grant ‘HABIT –

Crystal morphology from crystallographic and growthenvironment factors’ through EPSRC grant EP/I028293/1 andthe Synthonic Engineering programme supported by Pfizer,Boeringer-Ingellheim, Novartis and Syngenta. We are alsograteful to Dr. Kyrre Thalberg from Astra Zeneca (Sweden) forproviding terbutaline sulfate for this study.

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